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Accession Number N20120012844
Title Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils.
Publication Date 2012
Media Count 53p
Personal Author B. J. Lee M. S. Liou
Abstract This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.
Keywords Airfoils
Design optimization
Trajectory optimization

Source Agency National Aeronautics and Space Administration
NTIS Subject Category 51A - Aerodynamics
51C - Aircraft
Corporate Author National Aeronautics and Space Administration, Cleveland, OH. NASA John H. Glenn Research Center at Lewis Field.
Document Type Journal article
Title Note N/A
NTIS Issue Number 1303
Contract Number N/A

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